Question: Express this quotient in scientific notation: ${\frac{3.600\times 10^{2}} {9.0\times 10^{2}}}$
Answer: Start by collecting like terms together. $= {\frac{3.600} {9.0}} \times{\frac{10^{2}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.40 \times 10^{2\,-\,2}$ $= 0.40 \times 10^{0}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.40$ is the same as $4.00 \div 10$ , or $4.00 \times 10^{-1}$ $ = {4.00 \times 10^{-1}} \times 10^{0} $ $= 4.00\times 10^{-1}$